CN109000642A - A kind of improved strong tracking volume Kalman filtering Combinated navigation method - Google Patents
A kind of improved strong tracking volume Kalman filtering Combinated navigation method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
- G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
Abstract
The present invention is a kind of improved strong tracking volume Kalman filtering Combinated navigation method.Collect SINS system and GPS system output；Quantity of state and observed quantity are selected, SINS/GPS integrated navigation system state-space model is established；The initialization of SINS/GPS integrated navigation system；It updates and measures in the time that the k moment carries out standard CKF and update, obtain the error covariance value of a step status predication and the cross covariance value of one-step prediction；Using the improved strong tracking volume Kalman filtering algorithm for introducing strong tracking algorithm, fading factor after computed improved is simultaneously corrected the error covariance value of a step status predication；Using the step status predication after correction error covariance value carry out CKF measurement update, obtain the k+1 moment state estimation and with state error covariance.The present invention can improve the filtering accuracy of system, improve tracking ability when filter mutates to system mode, enhance the robustness of SINS/GPS integrated navigation system.
Description
Technical field
The present invention relates to a kind of Combinated navigation methods.
Background technique
Individual navigation system is difficult to meet the demand for the navigation system that the mankind are high for precision, stability is strong, and by two
Kind or two or more navigation system combine by some way constitute integrated navigation system can make navigate precision obtain
Very big promotion.Currently, the integrated navigation system being most widely used is strapdown inertial navigation system (Strapdown
Inertial Navigation System, SINS) and global positioning system (Global Position System, GPS),
SINS can make up that GPS anti-interference is poor, disadvantage of dynamic property deficiency；GPS can make up what SINS error accumulated at any time
Disadvantage.The advantages that independence, strong antijamming capability and GPS that can show SINS well be round-the-clock, high-precision, so
The application prospect of SINS/GPS integrated navigation system is considerable.
Most of integrated navigation system is all nonlinear in practical applications, and non-linear filtering method mainly has expansion
Open up Kalman filtering (Extended Kalman Filter, EKE), Unscented kalman filtering (Uncented Kalman
Filter, UKF), three kinds of filtering methods of volume Kalman filtering (Cubature Kalman Filter, CKF).EKF needs pair
Equation carries out Taylor series expansion and solves Jacobian matrix, computationally intensive, and carries out linearization approximate essence to nonlinear function
It spends not high.Disadvantages described above limits application of the EKF in nonlinear system.UKF is based on " comparing probability distribution progress approximation
Nonlinear function approximation is much easier " thought propose Unscented transform, mathematical theory is relatively weak.System is maintained for n,
UT needs to calculate 2n+1 sampled point during converting.And central point weight is different from other sampled point weights, when system is tieed up
When number is higher, central point sampled point weight is negative, it may appear that the case where covariance non-positive definite, so that filtering is difficult to be normally carried out.
CKF is the rule based on " three rank spherical surfaces-phase diameter seeks volume ", derives by strict mathematical formulae, n is maintained
System need to only calculate 2n sampled point.Compared to UKF, CKF can reduce calculation amount.The weight of all volume points of CKF is all identical and all
It is positive, therefore the case where be not in covariance non-positive definite during calculating.
In integrated navigation system, when the mathematical model and real system unmatched models or system of foundation mutate
When, it will lead to the phenomenon that filtering dissipates.For above situation, Zhou Huadong et al. based on the principle of orthogonality propose by force with
Track algorithm.Strong tracking algorithm is introduced into Kalman filter, online adjust gain matrix in real time guarantees have in filtering
Effect information all extracts, and allows the state of filter real-time tracking system, has stronger robustness.But traditional strong tracking
In algorithm, the selection of fading factor parameter is usually rule of thumb value；And under system health, strong tracking exists certain
Misjudgement probability.The above two o'clock influences the accuracy filtered.
Summary of the invention
Filtering accuracy can be improved the purpose of the present invention is to provide a kind of, when improving filter to system mode mutation
Tracking ability, enhance the improved strong tracking volume Kalman filtering Combinated navigation method of robustness.
The object of the present invention is achieved like this:
(1) data of actual measurement SINS system and GPS system output are collected；
(2) quantity of state and observed quantity are selected, SINS/GPS integrated navigation system state-space model is established；
(3) SINS/GPS integrated navigation system initializes；
(4) it updates and measures in the time that the k moment carries out standard CKF and update, obtain the error association side of a step status predication
The cross covariance value of difference and one-step prediction；
(5) using the improved strong tracking volume Kalman filtering algorithm for introducing strong tracking algorithm, after computed improved gradually
The factor that disappears simultaneously is corrected the error covariance value of a step status predication；
(6) it is updated using the measurement that the error covariance value of the step status predication after correction carries out CKF, when obtaining k+1
The state estimation at quarter and with state error covariance, the state estimation of complete paired systems.
The present invention may also include:
1, the SINS/GPS integrated navigation system state-space model of establishing specifically includes:
Select SINS/GPS integrated navigation system state variable:
Wherein,For attitude error；δVx,δVy,δVzFor velocity error；δ x, δ y, δ z are location error；For gyroscope constant value drift；For accelerometer constant value deviation,
State equation are as follows:
F () is nonlinear state equation；G (t) is that system noise drives battle array；W (t) indicates system noise, is white Gaussian
Noise, from the noise section of gyroscope and accelerometer, W (t) is indicated are as follows:
W (t)=[ωgx ωgy ωgz ωax ωay ωaz]T
Wherein ωgx,ωgy,ωgzRespectively represent the white noise in three axial directions of gyroscope, ωax,ωay,ωazIt respectively represents
White noise in three axial directions of accelerometer；
GPS system energy output position, velocity information；The position that the measurement of SINS/GPS integrated navigation system is exported by SINS
Set, the position of speed and GPS output, the difference subtracted each other of velocity information are constituted,
Position equation:
LI,λI,hILongitude, latitude, the location information in short transverse of respectively SINS output；LG,λG,hGRespectively
Longitude, latitude, the location information in short transverse of GPS output；HP(t) battle array, H are driven to measureP(t)=[03×6,I3×3,
03×6]；VPIt (t) is location error noise of the GPS receiver under navigational coordinate system,
Rate equation:
Wherein VIN,VIE,VIURespectively the east SINS, north, day direction output speed；VGN,VGE,VGURespectively GPS receiver
The speed that machine east, north, day direction export；HV(t) battle array, H are driven to measureV(t)=[03×3,diag{1,1,1},03×9]；VV(t)
The velocity error noise for being GPS receiver under navigational coordinate system,
The position and speed measurement equation of SINS and GPS is merged to obtain the total measurement equation of integrated navigation system:
2, it is described introduce strong tracking algorithm improved strong tracking volume Kalman filtering algorithm specifically includes the following steps:
Time updates:
(1) volume point is calculated
Wherein, m=2n, n are system mode dimension；Covariance matrixSkIt is PkCholesky decompose；[1] n dimension unit vector e=[1,0 ..., 0] is indicatedTChange the point set that the symbol of element carries out fully intermeshing generation,
[1]iI-th column of table set [1]；
(2) the volume point after state equation transmits is calculated
F () is mission nonlinear function；
(3) k+1 moment status predication value is calculatedWith state error covariance matrix
Wherein, the case where when subscript (l) is indicated that fading factor is not added, PXx, k+1 | kFor auto-covariance battle array, QkFor system
Noise variance matrix；
(4) updated state volume point is calculated
(5) the volume point after measurement equation transmits
(6) measurement predictor at k+1 moment is calculatedWith one-step prediction cross-correlation covariance matrix
(7) strong tracking algorithm, the fading factor λ after computed improved are introducedk+1, and calculate one-step prediction State error variance
Battle array Pk+1|k
λk+1=max (1, λ0)
Tr [] is indicated to Matrix Calculating mark in formula；λk+1For fading factor, work as λk+1When=1, STF does not just work, transformation
For the volume Kalman filtering of standard；Pxx,k+1|kFor the prediction variance matrix of the system noise variance matrix of consideration fading factor；
For the status predication variance matrix for not considering fading factor system noise variance matrix；For cross covariance battle array；ekNewly to cease residual error
Sequence,zk+1For substantial amount measured value,For estimated metrology value；β ' is the reduction factor；ρ is forgetting factor, is taken
Value is 0.95≤ρ≤0.995；Rk+1For measuring noise square difference battle array；
According to χ2Distribution table detects, and observes the relationship of dimension m and β ' are as follows:
Pk+1|k=λk+1Pxx,k+1|k+Qk
(8) it calculates to be added and improves fading factor λk+1More new state volume point afterwards
Pk+1|k=Sk+1|k(Sk+1|k)T
(9) the volume point after measurement equation transmits is calculated
It measures and updates:
(1) measurement predictor at k+1 moment is calculatedError in measurement covariance matrix Pzz,k+1|kWith one-step prediction cross-correlation
Covariance matrix Pxz,k+1|k
(2) the filtering gain matrix K at k+1 moment is calculatedk+1
Kk+1=Pxz,k+1|k(Pzz,k+1|k)-1
(3) state estimation at k+1 moment is calculated
(4) the state error covariance matrix P at k+1 moment is calculatedk+1
The present invention provides a kind of improved strong tracking volume Kalman filtering Combinated navigation methods, and STF is introduced into CKF
In, the calculation method of fading factor is improved using the knowledge of probability theory to reduce strong tracking probability of miscarriage of justice under normal circumstances.Root
According to χ2Distribution, reselects the parameter of fading factor.ISTCKF of the present invention is applied in SINS/GPS integrated navigation system, no
It is only capable of the filtering accuracy of raising system, moreover it is possible to tracking ability when filter mutates to system mode is improved, to enhance
The robustness of SINS/GPS integrated navigation system.
There are following advantages compared with existing technical method by the present invention:
(1) present invention combines improved Strong tracking filter with volume Kalman filtering, overcomes in SINS/GPS
When mutating in system because of model inaccuracy or system mode, CKF filters the case where dissipating.Improve the essence of filtering
Degree.
(2) ISTCKF filtering method of the present invention greatly reduces normal in system compared with traditional Strong tracking filter method
In the case of the probability judged by accident of strong tracking, and provide the fixed parameter value of fading factor, rather than only choose by rule of thumb.
(3) ISTCKF of the present invention is applied in SINS/GPS integrated navigation system, can enhance system to state mutation
Tracking ability enhances the robustness of SINS/GPS integrated navigation system.
Detailed description of the invention
Fig. 1 is improved strong tracking volume Kalman filtering Combinated navigation method schematic diagram of the invention；
Fig. 2 is the comparison of CKF of the present invention and tri- kinds of filtering method variances of EKF, UKF；
Fig. 3 is the comparison of CKF of the present invention and tri- kinds of filtering method filtering errors of EKF, UKF；
Fig. 4 (a) is using CKF filtering method attitude error, and Fig. 4 (b) is using CKF filtering method velocity error, Fig. 4
(c) for using CKF filtering method location error, Fig. 4 (d) is the comparison of posture and posture after filtering before filtering；
Fig. 5 (a) is ISTCKF filtering method attitude error of the present invention, and Fig. 5 (b) is to use the filtering side ISTCKF of the present invention
Method velocity error, Fig. 5 (c) are to use ISTCKF filtering method location error of the present invention, and Fig. 5 (d) is posture and filtering before filtering
The comparison of posture afterwards.
Specific embodiment
It illustrates below and the present invention is described in more detail.
In conjunction with Fig. 1, improved strong tracking volume Kalman filtering Combinated navigation method of the invention includes following step
It is rapid:
(1) data of actual measurement SINS system and GPS system output are collected；
(2) quantity of state and observed quantity are selected, SINS/GPS integrated navigation system state-space model is established；
(3) SINS/GPS integrated navigation system initializes；
(4) it updates and measures in the time that the k moment carries out standard CKF and update, obtain the error association side of a step status predication
The cross covariance value of difference and one-step prediction；
(5) using the improved strong tracking volume Kalman filtering algorithm for introducing strong tracking algorithm, after computed improved gradually
The factor that disappears simultaneously is corrected the error covariance value of a step status predication；
(6) it is updated using the measurement that the error covariance value of the step status predication after correction carries out CKF, when obtaining k+1
The state estimation at quarter and with state error covariance, the state estimation of complete paired systems.
A kind of improved strong tracking volume Kalman filtering Combinated navigation method of the present invention further include:
The SINS/GPS integrated navigation system model of establishing specifically includes:
Select SINS/GPS integrated navigation system state variable:
Wherein,For attitude error；δVx,δVy,δVzFor velocity error；δ x, δ y, δ z are location error；For gyroscope constant value drift；For accelerometer constant value deviation.
State equation are as follows:
F () is nonlinear state equation；G (t) is that system noise drives battle array；W (t) indicates system noise, is white Gaussian
Noise, from the noise section of gyroscope and accelerometer, W (t) be may be expressed as:
W (t)=[ωgx ωgy ωgz ωax ωay ωaz]T
ω in formulagx,ωgy,ωgzRespectively represent the white noise in three axial directions of gyroscope, ωax,ωay,ωazIt respectively represents
White noise in three axial directions of accelerometer.
GPS system energy output position, velocity information.The position that the measurement of SINS/GPS integrated navigation system is exported by SINS
It sets, the position of speed and GPS output, the difference subtracted each other of velocity information are constituted.
Position equation:
LI,λI,hILongitude, latitude, the location information in short transverse of respectively SINS output；LG,λG,hGRespectively
Longitude, latitude, the location information in short transverse of GPS output；HP(t) battle array, H are driven to measureP(t)=[03×6,I3×3,
03×6]；VPIt (t) is location error noise of the GPS receiver under navigational coordinate system.
Rate equation:
Wherein VIN,VIE,VIURespectively the east SINS, north, day direction output speed；VGN,VGE,VGURespectively GPS receiver
The speed that machine east, north, day direction export；HV(t) battle array, H are driven to measureV(t)=[03×3,diag{1,1,1},03×9]；VV(t)
The velocity error noise for being GPS receiver under navigational coordinate system.
The position and speed measurement equation merging of SINS and GPS can be obtained into the total measurement equation of integrated navigation system:
Described utilizes the improved strong tracking volume Kalman filtering algorithm (Improvement for introducing strong tracking algorithm
Strong Tracking Cubature Kalman Filter, ISTCKF) specific steps include:
Time updates:
(1) volume point is calculated
In formula, m=2n, n are system mode dimension；Covariance matrixSkIt is PkCholesky decompose；[1] n dimension unit vector e=[1,0 ..., 0] is indicatedTChange the point set that the symbol of element carries out fully intermeshing generation,
[1]iI-th column of table set [1].
(2) the volume point after state equation transmits is calculated
F () is mission nonlinear function.
(3) k+1 moment status predication value is calculatedWith state error covariance matrix
In formula, subscript (l) indicate without be added fading factor when the case where.PXx, k+1 | kFor auto-covariance battle array, QkFor system
Noise variance matrix.
(4) updated state volume point is calculated
(5) the volume point after measurement equation transmits
(6) measurement predictor at k+1 moment is calculatedWith one-step prediction cross-correlation covariance matrix
(7) strong tracking algorithm, the fading factor λ after computed improved are introducedk+1, and calculate one-step prediction State error variance
Battle array Pk+1|k
λk+1=max (1, λ0)
Tr [] is indicated to Matrix Calculating mark in formula；λk+1For fading factor, work as λk+1When=1, STF does not just work, transformation
For the volume Kalman filtering of standard；Pxx,k+1|kFor the prediction variance matrix of the system noise variance matrix of consideration fading factor；
For the status predication variance matrix for not considering fading factor system noise variance matrix；For cross covariance battle array；ekNewly to cease residual error
Sequence,zk+1For substantial amount measured value,For estimated metrology value；β ' is the reduction factor, can make filter effect
It is more smooth；ρ is forgetting factor, and general value is 0.95≤ρ≤0.995；Rk+1For measuring noise square difference battle array.
According to χ2Distribution table detects, and observes the relationship of dimension m and β ' are as follows:
Pk+1|k=λk+1Pxx,k+1|k+Qk
(8) it calculates to be added and improves fading factor λk+1More new state volume point afterwards
Pk+1|k=Sk+1|k(Sk+1|k)T
(9) the volume point after measurement equation transmits is calculated
It measures and updates:
(1) measurement predictor at k+1 moment is calculatedError in measurement covariance matrix Pzz,k+1|kWith one-step prediction cross-correlation
Covariance matrix Pxz,k+1|k
(2) the filtering gain matrix K at k+1 moment is calculatedk+1
Kk+1=Pxz,k+1|k(Pzz,k+1|k)-1
(3) state estimation at k+1 moment is calculated
(4) the state error covariance matrix P at k+1 moment is calculatedk+1
The present invention occurs using CKF filtering algorithm for SINS/GPS system model inaccuracy or system mode
The case where mutation, improves CKF filtering algorithm using strong tracking algorithm to enhance the robustness of system.And STCKF is filtered
Wave algorithm improves, with the precision of boostfiltering.So the present invention carries out emulation experiment using MATLAB simulation software, it will
CKF filtering algorithm is compared with existing nonlinear filtering algorithm EKF and UKF.
The embodiment of the present invention is used to explain the present invention, rather than limits the invention, in the spirit and right of invention
It is required that protection scope in, to any modifications and changes for making of the present invention, both fall within protection scope of the present invention.
Simulation analysis is carried out below with reference to specific example:
Assuming that object M is moved on a two-dimensional surface, uniformly accelrated rectilinear motion, Vertical Square are done in horizontal direction (x-axis)
Uniformly accelrated rectilinear motion is also done in (y-axis).Movement in both direction all has system noise Wk.False coordinate position is
(x0,y0) radar target M is tracked, then the distance between available radar and M rkWith target M relative to radar
AngleThe noise of radar is V (k).System noise is irrelevant with radar noise, and observation frequency is 50 times, sampling time T
=50s.
System noise W (k) variance matrix QkAre as follows:
Radar noise V (k) variance matrix RkAre as follows:
Position, speed and the acceleration for selecting a certain moment are state variable
Motion state equation are as follows:
X (k+1)=Φ X (k)+W (k)
State-transition matrix Φ in formula are as follows:
Observational equation are as follows:
Fig. 2, Fig. 3 are based on system above model, CKF and EKF, UKF filter effect comparison diagram；Wherein Fig. 2 be EKF,
The comparison of tri- kinds of filtering method variances of UKF, CKF；Fig. 3 is the comparison of tri- kinds of filtering method filtering errors of EKF, UKF, CKF；More than
Two width charts are bright, and EKF filter effect is worst, and CKF filter effect is best, and variance and error are all smaller.Illustrate the present invention to CKF
It is correct that filtering, which improves,.
Fig. 4 and Fig. 5 is the emulation that the measured data acquired based on SINS/GPS integrated navigation system is carried out.
Track used in emulating is the airborne movement generated using MATLAB program: the initial position longitude of aircraft is arranged
It is 126.63 °, latitude is 45.75 °.Navigational coordinate system is the output frequency that local geographic coordinate system sets SINS system guide information
Output frequency for 100Hz, GPS is 10Hz, and the data output frequencies of integrated navigation system are synchronous with SINS system.In addition, ground
Spherical model is taken as spheroid, and corresponding major semiaxis is Re=6378140m, semi-minor axis Rp=6356756m, ovality e=1/
298.27；Earth rotation angular speed is taken as ωie=7.2921158 × 10-5rad/s.The ginseng of gyroscope, accelerometer and GPS
Number setting is as shown in the table.
The parameter of 1 gyroscope of table, accelerometer and GPS
For the setting of model above parameter, SINS/GPS integrated navigation system is emulated, simulation time is
1312s.In 890s, system mode mutates, and carries out MTLAB emulation with CKF, ISTCKF respectively, simulation result such as Fig. 4,
It is Fig. 5, shown.Fig. 4 (a) is using CKF filtering method attitude error, and Fig. 4 (b) is using CKF filtering method velocity error, figure
4 (c) is, using CKF filtering method location error, Fig. 4 (d) are the comparison of posture and posture after filtering before filtering.Fig. 5 expression is adopted
The emulation carried out with ISTCKF filtering method of the invention.Fig. 5 (a) is ISTCKF filtering method attitude error of the present invention, Fig. 5
(b) to use ISTCKF filtering method velocity error of the present invention, Fig. 5 (c) is to be missed using ISTCKF filtering method of the present invention position
Difference, Fig. 5 (d) are the comparison of posture and posture after filtering before filtering.Obviously, either from posture, speed or the error of position
Figure it can be seen that, the method for the present invention is capable of the variation of tracking system state in time, improves system when system mutates
Filtering accuracy.
To sum up, a kind of improved strong tracking volume Kalman filtering Combinated navigation method of the present invention, navigation accuracy is high, and is
System strong robustness, method are simple, it is easy to accomplish.
Claims (3)
1. a kind of improved strong tracking volume Kalman filtering Combinated navigation method, it is characterized in that:
(1) data of actual measurement SINS system and GPS system output are collected；
(2) quantity of state and observed quantity are selected, SINS/GPS integrated navigation system state-space model is established；
(3) SINS/GPS integrated navigation system initializes；
(4) it updates and measures in the time that the k moment carries out standard CKF and update, obtain the error covariance value of a step status predication
With the cross covariance value of one-step prediction；
(5) using the improved strong tracking volume Kalman filtering algorithm for introducing strong tracking algorithm, after computed improved fade because
Son is simultaneously corrected the error covariance value of a step status predication；
(6) it is updated using the measurement that the error covariance value of the step status predication after correction carries out CKF, obtains the k+1 moment
State estimation and with state error covariance, the state estimation of complete paired systems.
2. improved strong tracking volume Kalman filtering Combinated navigation method according to claim 1, it is characterized in that described
SINS/GPS integrated navigation system state-space model is established to specifically include:
Select SINS/GPS integrated navigation system state variable:
Wherein,For attitude error；δVx,δVy,δVzFor velocity error；δ x, δ y, δ z are location error；
For gyroscope constant value drift；For accelerometer constant value deviation,
State equation are as follows:
F () is nonlinear state equation；G (t) is that system noise drives battle array；W (t) indicate system noise, for white Gaussian noise,
From the noise section of gyroscope and accelerometer, W (t) is indicated are as follows:
W (t)=[ωgx ωgy ωgz ωax ωay ωaz]T
Wherein ωgx,ωgy,ωgzRespectively represent the white noise in three axial directions of gyroscope, ωax,ωay,ωazRespectively represent acceleration
White noise in degree three axial directions of meter；
GPS system energy output position, velocity information；Position that the measurement of SINS/GPS integrated navigation system is exported by SINS,
The difference that the position of speed and GPS output, velocity information are subtracted each other is constituted,
Position equation:
LI,λI,hILongitude, latitude, the location information in short transverse of respectively SINS output；LG,λG,hGRespectively GPS is defeated
Longitude out, latitude, the location information in short transverse；HP(t) battle array, H are driven to measureP(t)=[03×6,I3×3,03×6]；VP
It (t) is location error noise of the GPS receiver under navigational coordinate system,
Rate equation:
Wherein VIN,VIE,VIURespectively the east SINS, north, day direction output speed；VGN,VGE,VGURespectively GPS receiver east,
The speed that north, day direction export；HV(t) battle array, H are driven to measureV(t)=[03×3,diag{1,1,1},03×9]；VVIt (t) is GPS
Velocity error noise of the receiver under navigational coordinate system,
The position and speed measurement equation of SINS and GPS is merged to obtain the total measurement equation of integrated navigation system:
3. improved strong tracking volume Kalman filtering Combinated navigation method according to claim 1 or 2, it is characterized in that institute
State introduce strong tracking algorithm improved strong tracking volume Kalman filtering algorithm specifically includes the following steps:
Time updates:
(1) volume point is calculated
Wherein, m=2n, n are system mode dimension；Covariance matrixSkIt is PkCholesky decompose；[1] n dimension unit vector e=[1,0 ..., 0] is indicatedTChange the point set that the symbol of element carries out fully intermeshing generation,
[1]iI-th column of table set [1]；
(2) the volume point after state equation transmits is calculated
F () is mission nonlinear function；
(3) k+1 moment status predication value is calculatedWith state error covariance matrix
Wherein, the case where when subscript (l) is indicated that fading factor is not added, PXx, k+1 | kFor auto-covariance battle array, QkFor system noise
Variance matrix；
(4) updated state volume point is calculated
(5) the volume point after measurement equation transmits
(6) measurement predictor at k+1 moment is calculatedWith one-step prediction cross-correlation covariance matrix
(7) strong tracking algorithm, the fading factor λ after computed improved are introducedk+1, and calculate one-step prediction State error variance battle array
Pk+1|k
λk+1=max (1, λ0)
Tr [] is indicated to Matrix Calculating mark in formula；λk+1For fading factor, work as λk+1When=1, STF does not just work, and is changed into mark
Quasi- volume Kalman filtering；Pxx,k+1|kFor the prediction variance matrix of the system noise variance matrix of consideration fading factor；For not
Consider the status predication variance matrix of fading factor system noise variance matrix；For cross covariance battle array；ekNewly to cease residual error sequence
Column,zk+1For substantial amount measured value,For estimated metrology value；β ' is the reduction factor；ρ is forgetting factor, is taken
Value is 0.95≤ρ≤0.995；Rk+1For measuring noise square difference battle array；
According to χ2Distribution table detects, and observes the relationship of dimension m and β ' are as follows:
Pk+1|k=λk+1Pxx,k+1|k+Qk
(8) it calculates to be added and improves fading factor λk+1More new state volume point afterwards
Pk+1|k=Sk+1|k(Sk+1|k)T
(9) the volume point after measurement equation transmits is calculated
It measures and updates:
(1) measurement predictor at k+1 moment is calculatedError in measurement covariance matrix Pzz,k+1|kWith one-step prediction cross-correlation association side
Poor battle array Pxz,k+1|k
(2) the filtering gain matrix K at k+1 moment is calculatedk+1
Kk+1=Pxz,k+1|k(Pzz,k+1|k)-1
(3) state estimation at k+1 moment is calculated
(4) the state error covariance matrix P at k+1 moment is calculatedk+1
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